Modelling Structural Dynamics for Control

A critical study of the process necessary to create structural control models is made. Exact closed-form solutions of beams and truss-beams continuous models open and closed loop dynamics are given, and used to evaluate the low frequency accuracy of hand prefined finite element models. For trusses condensed models and refined joint behavior are considered, using the equivalent continuum approach and a refined "midbay plane" approach. Updates of the continuous idealized model and the corresponding finite element model are considered, in cases where component and global dynamic properties are known. An analysis of modelling assumptions leads to sensitivity analyses, giving a better understanding of the origins and form of uncertainties in modal models. High modal density is considered as a major limiting factor for modal model accuracy, and is linked to structural symmetries and uncoupled local vibrations. The stability of input-output characteristics is studied for a damped truss subject to modal localization, and the desensitizing influence of damping is shown. To obtain small input-output state-space models of the structural dynamic response, a systematic treatment of modal truncation is introduced. Open and closed loop static corrections are considered for structures with and without rigid-body modes. Finally correction modes are introduced to completely represent the asymptotic low frequency behavior of truncated modes in both open and closed loop cases. Thesis Supervisor : Dr. Edward F. Crawley Title : Professor of Aeronautics and Astronautics Co-Thesis Supervisor: Dr. Andreas H. von Flotow Title : Professor of Aeronautics and Astronautics